312 On the Systems of Numerical Signs 



are quite different from those used in Sanscrit manuscripts, if 

 tlieflgureftif'^ is excepted. Who can say whether iHese 

 figures are not to be derived from the Tamul letters ? It is 

 true the figure for the group of a hundred is not to be found 

 among these letters, but the sign of the group of ten is to be 

 recognized in the letter ya, and the iivo in the letter u. Tne 

 numerical figures in the Teloogoa language, likewise spoken in 

 the southern districts of India within the Ganges*, which indi- 

 cate value by position, are in a strange manner different from 

 all other Indian figures, as far as they are known, in the signs 

 for 1, 8, and 9, whilst they agree with them in the figures of 

 S, 3, 4, and 6. The necessity jof expressing quantities by 

 writing has probably been felt sooner than that of writing 

 words, and therefore we may consider numerical figures as the 

 most ancient written characters. 



The instruments of palpable arithmetic, as they are called 

 in an ingenious work, the Philosophy of Arithmetic, by Mr. 

 Leslie, (1817,) in opposition to the figurative or graphic, are 

 both hands, heaps of pebbles (calculi, ■4/73(poi), grains of seed, 

 loose strings with knots (arithmetical strings, the quippos of 

 the Tartars and Peruvians), the suanpan put in a frame, the 

 table of the abacus, and the calculating machine of the Slavo- 

 nian nations with balls or grains of seed in files. All these in- 

 struments furnish to the eye the first graphic notations of 

 groups of a different degree. One hand, or a string with 

 knots or moveable balls, indicates the unities up to 5, or 10, 

 or 20. How often, by shutting of the single fingers, one hand 

 is gone through (7r£po9ra^£(y9a<), is indicated by the other hand, 

 of which every finger, that is, every unit, expresses a group of 

 five. Two loose strings with knots stand in the same relation 

 to One another. The calculation-strings, with moveable balls, 

 extended and fixed in a frame, or the ancient Asiatic suanpan, 

 which, in very ancient times, (perhaps by the Egyp]Li^^3, 

 at the time of the Pythagorean league,) was brought ta' the 



* Campbell's Grammar of the Teloogoa language, (Madras,) 1816. p., 4. 2,0^ 

 This is what formerly, bvit falsely, was called the Gentoo language. iBy the natives 

 it is. named Ti-itinga, or Telenga. With the table of the numerical figures in 

 Campbell's grammar, other varieties of Indian numerical characters tq be t'oynd 

 in Wahl's General History of the Oriental Languages, 1784, 3^ajby,i|i|^a^^',^^ 

 pared. 



